CN113220023B - High-precision real-time path planning method for unmanned aerial vehicle - Google Patents
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Abstract
The invention discloses a high-precision real-time path planning method for an unmanned aerial vehicle, and belongs to the field of precise control of unmanned aerial vehicles. The method comprises the following steps: s1: establishing a linear state differential equation of the unmanned aerial vehicle, and acquiring self constraint conditions and environment constraint conditions of the unmanned aerial vehicle; s2: establishing a kinematic error model of the unmanned aerial vehicle; s3: equivalently converting the solved problem into a linear equation solved problem; s4: setting a plurality of different unmanned aerial vehicle path targets according to environmental constraint conditions; s5: matrix decomposition is carried out by utilizing a deep learning method to solve control function parameters; s6: and judging whether the solved control parameters meet the self constraint conditions of the unmanned aerial vehicle. The method can greatly reduce the calculated amount, and can solve a plurality of targets by introducing a dynamic geometric method in real time and solve a high-precision control function by adopting a deep learning method so as to realize the real-time high-precision path planning of the unmanned aerial vehicle.
Description
Technical Field
The invention relates to a real-time path planning method for a high-precision unmanned aerial vehicle, belongs to the field of precise control of the unmanned aerial vehicle, and is particularly suitable for a multi-target high-precision path planning scene of the unmanned aerial vehicle.
Background
With the gradual maturity of unmanned aerial vehicle control technology, unmanned aerial vehicles have been widely applied to military and civil fields such as battlefield environmental reconnaissance, ground target striking, power line patrol, aerial photography and the like. Unmanned aerial vehicle path planning is especially important in unmanned aerial vehicle application. Common path planning methods can be classified into geometric methods, heuristic search methods, potential field methods, and the like. The geometric method firstly carries out geometric modeling on the environment, then selects a certain search algorithm to obtain a feasible solution according to a certain optimal strategy, but when the task space changes, the task space needs to be traversed again, and the calculated amount is large, so that the method is not suitable for dynamic track planning; the heuristic search method comprises classical algorithms such as an A-star algorithm, a particle swarm algorithm, a genetic algorithm and the like, and the calculation complexity of the algorithms is increased explosively along with the expansion of a search space, so that the instantaneity is poor; a typical method among the potential field methods is an artificial potential field method, which has advantages of reduced calculation amount and improved real-time performance, but is liable to fall into local optimization. Some methods are only suitable for offline planning, but external environmental factors are uncertain, and the unmanned aerial vehicle is limited by dynamic constraints such as maximum turning angle, detection radius and the like, so that the method has great limitation in the application process.
Although the calculation amount can be reduced and the real-time performance can be improved by improving or combining the above steps, the control precision is greatly sacrificed, and the multi-objective dynamic path planning problem cannot be completed.
Disclosure of Invention
The invention provides a high-precision unmanned aerial vehicle real-time path planning method, which attempts to convert an unmanned aerial vehicle path planning problem into a linear equation solving problem in an off-line mode, greatly reduces the calculated amount, solves multiple targets by introducing a dynamic geometric method in real time, and solves a high-precision control function by adopting a deep learning method so as to realize the high-precision path planning of an unmanned aerial vehicle.
In order to achieve the purpose, the invention provides the following technical scheme:
a high-precision unmanned aerial vehicle real-time path planning method comprises the following steps:
s1: establishing a linear state differential equation of the unmanned aerial vehicle based on a small disturbance linearization principle, and acquiring self constraint conditions and environment constraint conditions of the unmanned aerial vehicle;
s2: establishing an unmanned aerial vehicle kinematic error model by using an interpolation method;
s3: equivalently converting the problem solved by the unmanned aerial vehicle kinematic error model into a linear equation problem solved;
s4: setting a plurality of different unmanned aerial vehicle path targets according to environmental constraint conditions;
s5: taking the unmanned plane path target as a boundary condition to be brought into a linear equation of the unmanned plane, setting a control function type, and solving control function parameters by matrix decomposition by using a deep learning method;
s6: judging whether the solved control parameters meet self constraint conditions of the unmanned aerial vehicle or not, and if so, executing control flight; if not, deleting the solution, repeating the steps S5-S6 until no solution is met, correcting the unmanned aerial vehicle path target, repeating the steps S5-S6, and if no solution is still met and the upper limit of the calculation time is reached, performing path non-solution early warning.
Further, the linear state differential equation of the drone in step S1 is a constant coefficient differential equation in the form of: x' (t) = dx (t)/dt = a · x (t) + u (t), t ∈ [ t [ (/) 0 ，t f ]Wherein A is an nxn dimensional unmanned aerial vehicle state matrix and is determined according to a dynamic model of the unmanned aerial vehicle; u (t) is an n-dimensional steering vector with respect to time; x (t) is the state vector of the n-dimensional drone, and n is a positive integer, typically the drone speed, position, attitude angle, and so on.
Further, the interpolation method in the step S2 is a Hermit cubic spline interpolation method, and the Hermit cubic spline interpolation method belongs to the field of t in any time interval i ，t i+1 ]The sign expression of an approximate solution of the constant coefficient differential equation in any dimension in the step 1 can be obtained by an interpolation method
Wherein h is i ＝t i+1 -t i ，τ＝(t-t i )/h i ，α 0 (τ)＝2τ 3 -3τ 2 +1，α 1 (τ)＝τ 3 -τ 2 +τ，β 0 (τ)＝-2τ 3 +3τ 2 ，β 1 (τ)＝τ 3 -τ 2 ，τ∈[0，1]。
Furthermore, the interval of the Hermit cubic spline interpolation method is an equal-duration interval so as to greatly reduce the calculation amount, and the specific number i of the division sections can be adjusted according to the actual precision requirement.
Further, the kinematics of the unmanned aerial vehicle in the step S2 belongs to the [ t ] in the t E i ，t i+1 ]Error of the segment is
Further, quadratic modeling is carried out on the errors to obtain a kinematic error model of the unmanned aerial vehicle
Further, the step S3 specifically includes:
s301: for each segment
Substituting into Hermit cubic spline interpolation equation, and further obtaining a quadratic form of the sectional error
Wherein, y i ＝[x(t i )，x′(t i )，x(t i+1 )，x′(t i+1 )] T ，
b i ＝α 1 ′E-α 1 h i A，
d i ＝β′ 1 E-β 1 h i A and E are unit matrixes with dimensions of n multiplied by n;
s302: due to the fact that
Is constantly greater than 0 and is a constant when the control variable is determined, thus removing the term from the error quadratic form;
s303: converting the kinematic error model of the unmanned aerial vehicle into obj = min (y) T Fy-2 By), wherein F is (2 n · i +2 n) × (2 n · i +2 n) dimension represented By F i Corresponding superimposed moment ofThe matrix B is (2 n · i +2 n) dimensional represented by B i Corresponding to the superimposed vector, y = [ x (t) 0 )，x′(t 0 )，x(t 1 )，x′(t 1 )，…，x(t f )，x′(t f )] T Is (2 n · i +2 n) dimension y i Superposition of (2); where, x' (t) i ) Is x (t) i ) At t i The derivative of the time instant with respect to time t;
s304: when the rank is full, obj = min (y) T Fy-2 By) there is a unique solution, and the solution is Fy = B.
Further, step S4 specifically includes: according to the environmental constraint condition, path planning is carried out through a geometric method, the flying passing midpoint or state is selected as a path target, and the value is set as the path y = [ x (t) 0 )，x′(t 0 )，x(t 1 )，x′(t 1 )，…，x(t f )，x′(t f )] T A plurality of different drone path target values, i.e. part of the parameters in y, are known.
Further, the step S5 specifically includes:
s501: setting the type of a parameter-containing undetermined control function u (t) according to the requirement; usually, to reduce the amount of calculation and to ensure accuracy, a polynomial type with parameters with respect to time t is selected 1 or 2 times.
S502: solving Fy = B by using deep learning, and training parameters of a control function u (t); the method specifically comprises the following steps: (1) Substituting the random selected point in the interval range as the parameter of the control function into B to obtain
Solving for
To obtain
(2) Judgment of
Whether the values y of the corresponding elements from the plurality of path targets set in the step S4 all accord with the set error rangeAnd if the requirements are met, stopping training, outputting a control function, and if the requirements are not met, continuing training until the requirements are met. The deep learning technique generally employs a neural network.
Preferably, in the steps S1 to S3 of the present invention, the corresponding linear relationship matrix of the unmanned aerial vehicle may be obtained by using an offline calculation method, and then, the path target point solved by the dynamic environment geometric method is directly imported in the application by using an online method, so as to directly solve the optimal path control parameter.
Preferably, after the linear relation matrix is obtained through steps S1 to S3, the method of the present invention can be directly used to calculate the high-precision path of the known control function, i.e., known F and B, and solve for y.
In particular, the number of path targets, or the subdivision step h, may be increased for improved computational accuracy i However, the calculation amount is increased at the same time, and the error of the method of the present invention is the minimum under the condition that the time interval is divided by the same step size.
The invention has the beneficial effects that: the invention provides a high-precision unmanned aerial vehicle real-time path planning method, which converts a multi-target path planning problem with the minimum error of an unmanned aerial vehicle into a linear equation solving problem, greatly reduces the calculated amount, solves multiple targets by introducing a dynamic geometric method in real time, and solves a high-precision control function by adopting a deep learning method, thereby realizing the real-time high-precision path planning of the unmanned aerial vehicle.
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For the purpose and technical solution of the present invention, the present invention is illustrated by the following drawings:
FIG. 1 is a flow chart of a high-precision real-time path planning method for an unmanned aerial vehicle;
FIG. 2 is a schematic view showing the superposition of F and B in example 1 of the present invention.
Detailed Description
In order to make the purpose and technical solution of the present invention more clearly understood, the present invention will be described in detail with reference to the accompanying drawings and examples.
Example 1: matlab-based nobody published by Ronghui et alFor example, the unmanned aerial vehicle described in the "simulation analysis and research of mathematical model of the unmanned aerial vehicle" now needs to be controlled to execute t e [0, 10 ∈ [)]In the longitudinal flight in seconds, initially, all state variables are 0, and when the specific time t =5 seconds, the environmental constraint condition of the unmanned aerial vehicle is required to be that the flying speed is V (5) =1m/s 2 Pitch angle θ (5) =0 °, height H (5) =10m; the self-constraint condition is that the elevator deflection angle is not more than 30 degrees. The invention provides a high-precision real-time path planning method for an unmanned aerial vehicle, which comprises the following steps of:
s1: and establishing a linear state differential equation of the kinematics of the unmanned aerial vehicle based on a small disturbance linearization principle to obtain the state data of the unmanned aerial vehicle at the initial moment.
The longitudinal motion constant coefficient differential equation according to the article is shaped as: x' (t) = dx (t)/dt = a · x (t) + u (t),
wherein, A = A long The coefficient matrix is a 5 multiplied by 5 dimensional constant coefficient matrix and is determined according to a dynamic model of the unmanned aerial vehicle; u (t) = B long ·[δ e ，δ T ] T Is a control vector with respect to time; x (t) = [ V, alpha, q, theta, H] T The state vector of the unmanned aerial vehicle is shown, wherein V is flight speed, alpha is an attack angle, q is a pitch angle speed, theta is a pitch angle, and H is height.
S2: and (3) establishing an unmanned aerial vehicle kinematic error model by using an interpolation method. The method comprises the following specific steps:
first, the time interval is equally divided into 10 parts in units of 1 second, and for any part of h i ＝1；
Then, an interpolation method is adopted as a Hermit cubic spline interpolation method, and the t belongs to the [ t ] in any time interval i ，t i+1 ]The above method can obtain a symbolic expression of an approximate solution of the ordinary coefficient differential equation in step 1 in any dimension by interpolation
Wherein, tau = t-t i ，α 0 (τ)＝2τ 3 -3τ 2 +1，α 1 (τ)＝τ 3 -τ 2 +τ，β 0 (τ)＝-2τ 3 +3τ 2 ，β 1 (τ)＝τ 3 -τ 2 ，τ∈[0，1]；
And finally, constructing the kinematics of the unmanned aerial vehicle at t e [ t ∈ i ，t i+1 ]Error of the segment is
Further, quadratic modeling is carried out on the errors to obtain a kinematic error model of the unmanned aerial vehicle
S3: and equivalently converting the problem solved by the unmanned aerial vehicle kinematic error model into a linear equation problem solved. The method comprises the following specific steps:
s301: for each segment
Substituting into Hermit cubic spline interpolation equation, and further obtaining a quadratic form of the sectional error
Wherein, y i ＝[x(t i )，x′(t i )，x(t i+1 )，x′(t i+1 )] T ，
a i ＝α′ 0 E-α 0 A，b i ＝α′ 1 E-α 1 A，c i ＝β′ 0 E-β 0 A，d i ＝β′ 1 E-β 1 A and E are 5 multiplied by 5 dimensional identity matrixes;
s302: due to the fact that
Is constantly greater than 0 and is a constant when the control variable is determined, thus removing the term from the error quadratic;
s303: unmanned aerial vehicle kinematic error model is converted into obj = min (y) T Fy-2 By), wherein F is 110 x 110 dimensions and is defined By F i In (1) pairShould superpose the matrix, B is 110 dimension from B i Corresponding to the superimposed vector, y = [ x (t) 0 )，x′(t 0 )，x(t 1 )，x′(t 1 )，…，x(t f )，x′(t f )] T Is 110 dimensions y i Superposition of (2);
s304: f is full rank and is a band matrix, obj = min (y) T Fy-2 By) there is a unique solution, and the solution is Fy = B.
S4: and setting a plurality of different unmanned aerial vehicle path targets according to the environmental constraint conditions. The method specifically comprises the following steps:
importing all data of the initial conditions x (0) and x '(0) and partial known environment data in x (5) into y = [ x (0), x' (0), x (1), x '(1), \ 8230;, x (10), x' (10) according to environment constraint conditions] T 。
S5: taking the unmanned aerial vehicle path target as a boundary condition to be brought into a linear equation of the unmanned aerial vehicle, setting a control function type, and solving control function parameters by matrix decomposition by using a deep learning method. The method comprises the following specific steps:
s501: setting a piecewise function containing 10 sections of parameter pending control functions u (t) according to requirements, wherein the ith section is u (t) = B long ·[a i t 2 +b i t+c i ，d i t 2 +e i t+f i ] T ，a i 、b i 、c i 、d i 、e i 、f i Are parameters to be determined.
S502: solving Fy = B by using a neural network, and training parameters of a control function u (t); the method specifically comprises the following steps: (1) Substituting the random selected point in the interval range as the parameter of the control function into B to obtain
Solving for
To obtain
(2) Judgment of
And (3) whether all data of the corresponding elements from the initial conditions x (0) and x' (0) and part of known environment data in x (5) meet the set error range requirement or not, stopping training if the data meet the set error range requirement, outputting a control function, and continuing training until the data meet the set error range requirement if the data do not meet the set error range requirement.
S6: judging whether the deviation angle of the elevator calculated by the solved control parameters meets the self constraint condition of the unmanned aerial vehicle, namely whether the deviation angle of the elevator is not more than 30 degrees or not, and if so, executing control flight; if the unmanned aerial vehicle does not meet the preset computation time upper limit, deleting the solutions, and re-executing the step S5 for computation until the unmanned aerial vehicle self constraint condition is met, and then executing flight, or reaching the preset computation time upper limit and outputting no-solution early warning.
Example 2: similarly, taking an unmanned plane described in "math model simulation analysis and research based on Matlab unmanned plane" published by honor et al as an example, it is now necessary to control the unmanned plane to execute t ∈ [0, 10 ∈ [ c ]]In the longitudinal flight in seconds, initially, all state variables are 0, and u (t) = B is planned to be adopted long ·[t 2 +2t，2t] T As a control vector, all states of the unmanned aerial vehicle in the flight process need to be predicted. The invention provides a high-precision unmanned aerial vehicle real-time path planning method, which comprises the following steps:
s1: establishing a kinematic linear state differential equation of the unmanned aerial vehicle, and acquiring self constraint conditions and environmental constraint conditions of the unmanned aerial vehicle;
s2: establishing an unmanned aerial vehicle kinematic error model by using an interpolation method;
s3: equivalently converting the problem solved by the unmanned aerial vehicle kinematic error model into a linear equation problem solved;
s4: and substituting the initial conditions and the control vectors into a linear equation to solve to obtain all states of the unmanned aerial vehicle in the flight process.
Finally, it is noted that the above-mentioned preferred embodiments illustrate rather than limit the invention, and that, while the invention has been described in detail with reference to the above-mentioned preferred embodiments, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the scope of the invention as defined by the appended claims.
Claims (8)
1. A high-precision unmanned aerial vehicle real-time path planning method is characterized by comprising the following steps:
s1: establishing a linear state differential equation of the unmanned aerial vehicle based on a small disturbance linearization principle, and acquiring self constraint conditions and environment constraint conditions of the unmanned aerial vehicle;
s2: establishing an unmanned aerial vehicle kinematic error model by using an interpolation method;
s3: equivalently converting the problem solved by the unmanned aerial vehicle kinematic error model into a linear equation problem solved;
s4: setting a plurality of different unmanned aerial vehicle path targets according to environmental constraint conditions;
s5: taking the unmanned plane path target as a boundary condition to be brought into a linear equation of the unmanned plane, setting a control function type, and solving control function parameters by matrix decomposition by using a deep learning method;
s6: judging whether the solved control parameters meet the self constraint conditions of the unmanned aerial vehicle or not, and if so, executing control flight; if not, deleting the solution, repeating the steps S5-S6 until no solution is met, correcting the unmanned aerial vehicle path target, repeating the steps S5-S6, and if no solution is still met and the upper limit of the calculation time is reached, performing path non-solution early warning.
2. The method according to claim 1, wherein a is an nxn dimensional unmanned plane state matrix determined according to a dynamical model of the unmanned plane; u (t) is an n-dimensional control vector with respect to time; and x (t) is the state vector of the n-dimensional unmanned aerial vehicle.
3. The real-time path planning method for the high-precision unmanned aerial vehicle as claimed in claim 1, wherein the interpolation method in step S2 is Hermit cubic spline interpolation method, and t e [ t ] is an arbitrary time interval i ，t i+1 ]Go up throughThe interpolation method can obtain a symbolic expression of an approximate solution of the linear state differential equation in step S1 in any dimension
Wherein h is i ＝t i+1 -t i ，τ＝(t-t i )/h i ，α 0 (τ)＝2τ 3 -3τ 2 +1，α 1 (τ)＝τ 3 -τ 2 +τ，β 0 (τ)＝-2τ 3 +3τ 2 ，β 1 (τ)＝τ 3 -τ 2 ，τ∈[0，1]。
4. The real-time path planning method for the high-precision unmanned aerial vehicle as claimed in claim 3, wherein the interval of the Hermit cubic spline interpolation method is an interval with an equal duration so as to greatly reduce the calculation amount, and the specific number i of the division sections can be adjusted according to actual precision requirements.
5. The method according to claim 1, wherein the kinematics of the UAV of step S2 is at te [ t ∈ [ t ] i ，t i+1 ]Error of the segment is
Further, quadratic modeling is carried out on the errors to obtain a kinematic error model of the unmanned aerial vehicle
6. The method for planning the real-time path of the high-precision unmanned aerial vehicle according to claim 1, wherein the step S3 specifically comprises:
s301: for each segment
Substituted Hermit cubic spline interpolationValue equation, and further, obtaining quadratic form of segment error
Wherein, y i ＝[x(t i )，x′(t i )，x(t i+1 )，x′(t i+1 )] T ，
b i ＝α 1 ′E-α 1 h i A，
d i ＝β 1 ′E-β 1 h i A；
S302: due to the fact that
Is constantly greater than 0 and is a constant when the control variable is determined, thus removing the term from the error quadratic;
s303: unmanned aerial vehicle kinematic error model is converted into obj = min (y) T Fy-2 By), wherein F is F i Is a corresponding superposition of B i Corresponding superposition of (c), y = [ x (t) 0 )，x′(t 0 )，x(t 1 )，x′(t 1 )，…，x(t f )，x′(t f )] T Is y i Superposition of (2);
s304: when the rank is full, obj = min (y) T Fy-2 By) there is a unique solution, and the solution is Fy = B.
7. The real-time path planning method for the high-precision unmanned aerial vehicle according to claim 1, wherein the step S4 is specifically as follows: planning a path by a geometric method according to environmental constraint conditions, and setting a path y = [ x (t) 0 )，x′(t 0 )，x(t 1 )，x′(t 1 )，…，x(t f )，x′(t f )] T A plurality of different drone path target values, i.e. part of the parameters in y, are known.
8. The method for planning the real-time path of the high-precision unmanned aerial vehicle according to claim 1, wherein the step S5 specifically comprises:
s501: setting the type of a parameter-containing undetermined control function u (t) according to the requirement;
s502: solving Fy = B by using deep learning, and training parameters of a control function u (t); the method comprises the following specific steps: (1) Substituting the random selected point in the interval range as the parameter of the control function into B to obtain
Solving for
To obtain
(2) Judgment of
And if the error range requirements of the set multiple different unmanned aerial vehicle path targets are met, stopping training, outputting a control function, and if the error range requirements are not met, continuing training until the error range requirements are met.
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